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We study the problem of capacity modification in the many-to-one stable matching of workers and firms. Our goal is to systematically study how the set of stable matchings changes when some seats are added to or removed from the firms. We make three main contributions: First, we examine whether firms and workers can improve or worsen upon changing the capacities under worker-proposing and firm-proposing deferred acceptance algorithms. Second, we study the computational problem of adding or removing seats to either match a fixed worker-firm pair in some stable matching or make a fixed matching stable with respect to the modified problem. We develop polynomial-time algorithms for these problems when only the overall change in the firms' capacities is restricted, and show NP-hardness when there are additional constraints for individual firms. Lastly, we compare capacity modification with the classical model of preference manipulation by firms and identify scenarios under which one mode of manipulation outperforms the other. We find that a threshold on a given firm's capacity, which we call its peak, crucially determines the effectiveness of different manipulation actions.

Probabilistic concurrent/distributed strategies have so far not been investigated thoroughly in the context of imperfect information, where the Player has only partial knowledge of the moves made by the Opponent. In a situation where the Player and Opponent can make concurrent moves according to the game, and the Player cannot see the move of the Opponent, the move of the Player should be probabilistically independent of the move of the Opponent. What has been achieved is showing a bijection between strategies on a game with algebra and strategies on a regular (albeit more complex) game. We also succeeded in showing the results holds with neutral events. However it is still unclear if a well-formed bicategory of concurrent games with algebras can be defined. Our attempts to compose these strategies while managing the added structure didn't pan out. Concerning the other classic extensions of concurrent games the first results we presented show promise of a more general usage of games with algebra.

As IoT networks become more complex and generate massive amounts of dynamic data, it is difficult to monitor and detect anomalies using traditional statistical methods and machine learning methods. Deep learning algorithms can process and learn from large amounts of data and can also be trained using unsupervised learning techniques, meaning they don't require labelled data to detect anomalies. This makes it possible to detect new and unknown anomalies that may not have been detected before. Also, deep learning algorithms can be automated and highly scalable; thereby, they can run continuously in the backend and make it achievable to monitor large IoT networks instantly. In this work, we conduct a literature review on the most recent works using deep learning techniques and implement a model using ensemble techniques on the KDD Cup 99 dataset. The experimental results showcase the impressive performance of our deep anomaly detection model, achieving an accuracy of over 98\%.

In optimization-based approaches to inverse problems and to statistical estimation, it is common to augment criteria that enforce data fidelity with a regularizer that promotes desired structural properties in the solution. The choice of a suitable regularizer is typically driven by a combination of prior domain information and computational considerations. Convex regularizers are attractive computationally but they are limited in the types of structure they can promote. On the other hand, nonconvex regularizers are more flexible in the forms of structure they can promote and they have showcased strong empirical performance in some applications, but they come with the computational challenge of solving the associated optimization problems. In this paper, we seek a systematic understanding of the power and the limitations of convex regularization by investigating the following questions: Given a distribution, what is the optimal regularizer for data drawn from the distribution? What properties of a data source govern whether the optimal regularizer is convex? We address these questions for the class of regularizers specified by functionals that are continuous, positively homogeneous, and positive away from the origin. We say that a regularizer is optimal for a data distribution if the Gibbs density with energy given by the regularizer maximizes the population likelihood (or equivalently, minimizes cross-entropy loss) over all regularizer-induced Gibbs densities. As the regularizers we consider are in one-to-one correspondence with star bodies, we leverage dual Brunn-Minkowski theory to show that a radial function derived from a data distribution is akin to a ``computational sufficient statistic'' as it is the key quantity for identifying optimal regularizers and for assessing the amenability of a data source to convex regularization.

In social recommender systems, it is crucial that the recommendation models provide equitable visibility for different demographic groups, such as gender or race. Most existing research has addressed this problem by only studying individual static snapshots of networks that typically change over time. To address this gap, we study the evolution of recommendation fairness over time and its relation to dynamic network properties. We examine three real-world dynamic networks by evaluating the fairness of six recommendation algorithms and analyzing the association between fairness and network properties over time. We further study how interventions on network properties influence fairness by examining counterfactual scenarios with alternative evolution outcomes and differing network properties. Our results on empirical datasets suggest that recommendation fairness improves over time, regardless of the recommendation method. We also find that two network properties, minority ratio, and homophily ratio, exhibit stable correlations with fairness over time. Our counterfactual study further suggests that an extreme homophily ratio potentially contributes to unfair recommendations even with a balanced minority ratio. Our work provides insights into the evolution of fairness within dynamic networks in social science. We believe that our findings will help system operators and policymakers to better comprehend the implications of temporal changes and interventions targeting fairness in social networks.

A better understanding of interactive pedestrian behavior in critical traffic situations is essential for the development of enhanced pedestrian safety systems. Real-world traffic observations play a decisive role in this, since they represent behavior in an unbiased way. In this work, we present an approach of how a subset of very considerable pedestrian-vehicle interactions can be derived from a camera-based observation system. For this purpose, we have examined road user trajectories automatically for establishing temporal and spatial relationships, using 110h hours of video recordings. In order to identify critical interactions, our approach combines the metric post-encroachment time with a newly introduced motion adaption metric. From more than 11,000 reconstructed pedestrian trajectories, 259 potential scenarios remained, using a post-encroachment time threshold of 2s. However, in 95% of cases, no adaptation of the pedestrian behavior was observed due to avoiding criticality. Applying the proposed motion adaption metric, only 21 critical scenarios remained. Manual investigations revealed that critical pedestrian vehicle interactions were present in 7 of those. They were further analyzed and made publicly available for developing pedestrian behavior models3. The results indicate that critical interactions in which the pedestrian perceives and reacts to the vehicle at a relatively late stage can be extracted using the proposed method.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.

Deep neural networks have achieved remarkable success in computer vision tasks. Existing neural networks mainly operate in the spatial domain with fixed input sizes. For practical applications, images are usually large and have to be downsampled to the predetermined input size of neural networks. Even though the downsampling operations reduce computation and the required communication bandwidth, it removes both redundant and salient information obliviously, which results in accuracy degradation. Inspired by digital signal processing theories, we analyze the spectral bias from the frequency perspective and propose a learning-based frequency selection method to identify the trivial frequency components which can be removed without accuracy loss. The proposed method of learning in the frequency domain leverages identical structures of the well-known neural networks, such as ResNet-50, MobileNetV2, and Mask R-CNN, while accepting the frequency-domain information as the input. Experiment results show that learning in the frequency domain with static channel selection can achieve higher accuracy than the conventional spatial downsampling approach and meanwhile further reduce the input data size. Specifically for ImageNet classification with the same input size, the proposed method achieves 1.41% and 0.66% top-1 accuracy improvements on ResNet-50 and MobileNetV2, respectively. Even with half input size, the proposed method still improves the top-1 accuracy on ResNet-50 by 1%. In addition, we observe a 0.8% average precision improvement on Mask R-CNN for instance segmentation on the COCO dataset.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.